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 Mar 22 awarded Yearling Aug 26 asked Geodesics of Sasaki metric Aug 5 comment Normal curvature of geodesic spheres Dear @NormalHuman, this is a nice example, thank you. I can't see if it is possible for this example to be the universal covering of a compact Riemannian manifold. If it is not, perhaps I can have some hope. I'm interested in investigate this Lipschitz constant in universal coverings of compact Riemannian manifolds without conjugate points. Aug 4 comment Normal curvature of geodesic spheres Hi, @AntonPetrunin, indeed. Allow me to go a little further on my question. I see that if I fix the radius $R$, the normal vector is Lipschitz as you pointed out, and it appears to me that the Lipschitz constant $L$ will depend on $R$. Letting the radius $R>1$ be arbitrary large (in the abscense of conjugate points), do you have any feeling on if it is possible to have some upper bound for the Lipschitz constants? Aug 3 revised Normal curvature of geodesic spheres edited tags Aug 3 asked Normal curvature of geodesic spheres Mar 22 awarded Yearling Feb 24 comment a.e.-defined integrable functions on $X$. I think the answer is the following: let us denote the domain of the function $f$ by $D(f)\subset X$. The expression "a.e.-defined integrable functions on $X$" means that $\mu\big(X-D(f)\big)=0$ and $f$ is integrable in $D(f)$ Feb 13 asked Landsberg angle Jan 18 comment Bi-asymptotic geodesics in Visibility manifolds Thanks again. Our conversations on the subject have opened my eyes for several points on this theory. Jan 18 accepted Bi-asymptotic geodesics in Visibility manifolds Jan 13 comment Bi-asymptotic geodesics in Visibility manifolds I see. It doesn't help. I can consider just $\mathbb{H}^2\times\mathbb{R}$. Jan 13 comment Bi-asymptotic geodesics in Visibility manifolds I have in addition the abscense of conjugate points, if it helps... Jan 13 revised Bi-asymptotic geodesics in Visibility manifolds added 40 characters in body Jan 13 comment Bi-asymptotic geodesics in Visibility manifolds Yes, you are completely right. I have wrote (and after I deleted it) the non-compact condition, but I thought it was perhaps unnecessary to comment. I will put this there to make more sense to the question. Thanks again! Jan 13 asked Bi-asymptotic geodesics in Visibility manifolds Oct 8 awarded Tumbleweed Oct 1 revised Deck transformations and Gromov Hyperbolicity added 103 characters in body Oct 1 asked Deck transformations and Gromov Hyperbolicity Aug 11 revised Gromov hyperbolic metric spaces are quasi-convex deleted 76 characters in body